Operations with Polynomials

Polynomial Terminology

100

Name the Expression by Degree and Number of Terms: (if an expression has more than a degree of 4, use a number to describe the degree ex: 9th degree)

4x² +3x

Quadratic Binomial

200

Name the Expression by Degree and Number of Terms: (if an expression has more than a degree of 4, use a number to describe the degree ex: 9th degree)

6x^3y^2z

6th degree Monomial

300

Name the Expression by Degree and Number of Terms: (if an expression has more than a degree of 4, use a number to describe the degree ex: 9th degree)

3x^4+2x^3-5

Quartic Trinomial

400

Name the Expression by Degree and Number of Terms: (if an expression has more than a degree of 4, use a number to describe the degree ex: 9th degree)

16x^3+8x^2+4x+2

Cubic Polynomial

500

Name the Expression by Degree and Number of Terms: (if an expression has more than a degree of 4, use a number to describe the degree ex: 9th degree)

4

Constant monomial

Adding Polynomials

100

What is the sum of the following polynomial:

(5x^2+3x -6) + (3x^2 -x + 5)

8x^2 -2x -1

200

What is the sum of the following polynomial:

(x^2 -x +5) + (6x^2 +2x -10)

7x^2 + x -5

300

What is the sum of the following polynomial:

(4y^2 + 8y -12) + ( 3y^3 - 13y +5)

3y^3 +4y^2 -5y-7

400

What is the sum of the following polynomial:

(6a^3+12a^2-15a)+(4a^2 - 12a +8)

6a^3 +16a^2 -27a +8

500

What is the sum of the following polynomial:

(3x^2 -5x +7) + (x^2 + 2x -1)

4x^2 -3x +6

Subtracting Polynomials

100

What is the difference between the following polynomials:

(5x^2 +3x-6)-(3x^2 -x +5)

2x^2 +4x-11

200

What is the difference between the following polynomials:

(a^3-2a^2)-(3a^2-4a^3)

5a^3-5a^2

300

What is the difference between the following polynomials:

(6x^2 -3x +4)-(-2x^2 +2x-2)

8x^2 -5x +6

400

What is the difference between the following polynomials:

(5x - 2) - (7x -3)

-2x +1

500

What is the difference between the following polynomials: 

(3x^2 +8x-4)-(2x^2+5x-9)

x^2 +3x +5

Multiplying Polynomials

100

Evaluate:

4(7x - 4)

28x-16

200

Evaluate:

4x(3x^2 + 4x +10)

12x^3 +16x^2 +40x

300

Evaluate:

(2x+1)(-3x+5)

-6x^2+7x+5

400

Evaluate

(x+3)(x^2+2x+4)

x^3+5x^2+10x+12

500

Evaluate:

(x+5)(x^2 -2x+9)

x^3+3x^2-1x+45

Polynomials in Context

100

A triangle has the following 3 sides, what is the perimeter of the triangle?

x^2+4x + 2, x^2 +5x -4, and 5x^2 + 3x + 4

7x^2+12x+2

200

A rectangle has a length of 3x and a width of 2x+1. What is the area?

6x^2+3x

300

What is the perimeter of my garden?

10x+6

400

What is the area of my garden?

6x^2+14x-40

500

You made a box and the perimeter was 3x, then you made another box and the perimeter was 2x - 1. What is the difference between the perimeter of your first and second box?

x-1

Special Products

100

Evaluate:

(3x^2+4)²

9x^4+24x^2+16

200

Evaluate:

(2x³-3y)²

4x^6-12x^3y+9y²

300

Evaluate:

(3x-4)(3x+4)

9x²-16

400

What product describes the pattern for a Square of Sums? Use "a" and "b" as variables to describe the polynomial expression

a^2+2ab+b²

500

What product describes the pattern for a Difference of Squares? Use "a" and "b" as variables to describe the polynomial expression

a²-b²